This invention relates to an imaging optical system using index distribution type optical elements, and in particular to an imaging optical system suitable as the optical system of a business machine such as a copying apparatus or a facsimile apparatus.
In the optical system of a business machine such as a copying apparatus or a facsimile apparatus, a double-eye optical system of erect one-to-one magnification such as Selfoc (the trade name of a product of Japan Sheet Glass Co., Ltd.) has heretofore been used as an imaging optical system, instead of a single spherical lens system, thereby achieving compactness of the apparatus. Where optical elements of such index distribution type, i.e., the so-called radial index distribution type which is an index distribution radially symmetrical about the optic axis, are arranged in the form of an array, it is practised to arrange index distribution type optical element arrays in two rows proximate to each other and in staggered relationship, as shown, for example, in Japanese Utility Model Publication No. 59-9230 in order to eliminate irregularity of the quantity of light on the image surface. However, the use of a plurality of rows of arrays leads to a great number of optical elements, which in turn leads to a high cost and further to the necessity of very high accuracy of arrangement and difficulties in manufacture.
So, it has heretofore been desired to arrange a plurality of index distribution type optical elements in a row to thereby make an imaging optical system of erect one-to-one magnification, and U.S. Pat. No. 4,719,488 shows an imaging optical system of a construction in which index distribution type optical elements are densely arranged in a row. FIG. 1 of the accompanying drawings illustrates the imaging optical system of U.S. Pat. No. 4,719,488. Index distribution type optical elements 10 are arranged in a row, and light fluxes from the optical elements 10 are superposed one upon another and imaged on the imaging plane. However, in this example of the prior art, to minimize the arrangement pitch irregularity of the quantity of light, it has been necessary to suppress the degree of superposition Mo as follows: ##EQU2## where x is 0 or greater integer and Xo is the field radius of said optical elements and D is the effective diameter of said optical elements. Where at this time, the conjugate length TC has been determined by mechanical arrangement conditions, there is the following relation: ##EQU3## where n.sub.o is the central refractive index of the index distribution, and therefore the length Zo of the optical elements can only assume desultory values in conformity with the desultory Mo of formula (1), and it has been difficult to adjust Mo to the length of the optical elements which is optimum in terms of aberrations for the index distribution characteristic of the optical elements. Also, conversely, if the length Zo of the optical elements is determined so that the aberration characteristic becomes optimum under a certain index distribution (the central refractive index is n.sub.o and the secondary distribution constant is g), the degree of superposition Mo is ##EQU4## and therefore, there is not provided a degree of superposition conforming to the condition (1), and this has led to the disadvantage that although it is good in terms of aberrations, the pitch irregularity of the quantity of light becomes great.
Also, U.S. Pat. No. 4,349,248 and U.S. Pat. No. 4,373,780 show imaging optical systems of a construction in which index distribution type optical elements are arranged in a row at predetermined intervals, but in these imaging optical systems, the pitch irregularity of the quantity of light occurs and a desired imaging performance is not obtained.